Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I think this answers my question. I guess that we can now invert all the rest of the primes but one. So we can take $p_0$ to be the prime we don't want to invert. I assume that if we take a UFD and invert all but one of the remaining primes, we still get a UFD.